Formation energies of rutile metal dioxides using density functional theory

We apply standard density functional theory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially the formation energy of the oxygen molecule and the electron self-interaction for localized d and f electrons are known shortcomings. In this paper we show that despite the known problems, it is possible to calculate the stability of a wide range of rutile oxides MO2, with M being Pt, Ru, Ir, Os, Pb, Re, Mn, Se, Ge, Ti, Cr, Nb, W, Mo, and V, using the electrochemical series as reference. The mean absolute error of the formation energy is 0.29 eV using the revised Perdew-Burke-Ernzerhof (PBE) GGA functional. We believe that the reason for the success is due to the reference level being H-2 and H2O and not O-2 and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides they are not included in this study. We show that the variations in formation energy can be understood in terms of a previously suggested model separating the formation energy into a metal deformation contribution and an oxygen binding contribution. The latter is found to scale with the filling of the d band.